Pitts inequalities and uncertainty principle for generalized fourier transform

We study the two-parameter family of unitary operators (equation presented) which are called (κ, a)-generalized Fourier transforms and defined by the a-deformed Dunkl harmonic oscillator δk,a = |x|2-aδκ -|x|a, a > 0, where δk is the Dunkl Laplacian. Particular cases of such operators are the...

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Detalles Bibliográficos
Autores: Gorbachev, D.V., Ivanov, V.I., Tikhonov, S.Y.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/445763
Acceso en línea:http://hdl.handle.net/2072/445763
Access Level:acceso abierto
Palabra clave:51
Descripción
Sumario:We study the two-parameter family of unitary operators (equation presented) which are called (κ, a)-generalized Fourier transforms and defined by the a-deformed Dunkl harmonic oscillator δk,a = |x|2-aδκ -|x|a, a > 0, where δk is the Dunkl Laplacian. Particular cases of such operators are the Fourier and Dunkl transforms. The restriction of Fk,a to radial functions is given by an a-deformed Hankel transform Hλ,a. We obtain necessary and sufficient conditions for the weighted (Lp, Lq) Pitt inequalities to hold for the a-deformed Hankel transform. Moreover, we prove two-sided Boas-Sagher type estimates for the general monotone functions. We also prove sharp Pitts inequality for Fk,a transform in L2(ℝd) with the corresponding weights. Finally, we establish the logarithmic uncertainty principle for Fk,a. © The Author(s) 2016.

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